We did not find an easily accessible visualization of the relationship between the z^2+c julia sets and the mandelbrot set. The mandelbrot set acts as an index into the julia set where you can characterize the behavior of the corresponding julia sets in different parts of the mandelbrot set.
What it does
Displays the mandelbrot set and clicking on various regions will display a julia set corresponding to that region.
How we built it
started with simple octave generation of julia and mandelbrot sets. moved on to utilizing an efficient c++ implementation to mass generate julia sets (to avoid on demand generation, client side or server side)
Mass-generated thousands of detailed images of julia set images over 12 hours to build a fast, on-demand database for high-level viewing of the mandelbrot-julia set relationship.
Challenges we ran into
Ended up wasting 6 hours trying to build a project due to random dependancy issues and sleepiness.
Accomplishments that we're proud of
ability to get a large data set generated in this short amount of time
What we learned
ubuntu's packages are so out of date
What's next for Mandelbrot Explorer
expand the visulization to zoom in dynamically with server-side or client side generation, saving results for future expanding database
Technical Complexity mass generation of many fractals was an interesting challenge, we ended up not having enough computing power with two alien wares laptops, set up AWS to mass generate many more and a system to generate over 50k images for the project.
Polish The website is functional, not super pretty but it does what it needs to do! Originality Usefulness - General This would be useful for curious people exploring fractals in general Usefulness - Nonprofit A visulization like this would be helpful in complex analysis and other classes for universities. (non proffit)